Spivak, Calculus and Answer Book to Calculus
4th ed. xvi + 680 pages.
Combined Answer Book to Calculus, Third and Fourth editions.
ii + 448 pages.
Click here for selections from the Preface Return to book list Return to home page
Written as a textbook, Calculus is used both for theoretical calculus courses and for "Introduction to Analysis" courses in several U.S. universities. It is also used (in rather larger numbers) in quite a few Canadian universities, as well as in a few universities overseas. Because of this, sales of the Answer Book, which are intended for instructors of the courses, are normally restricted.
Calculus has also found an audience among individuals learning, or
relearning, the material on their own.
(Some reader reviews may be found on the Amazon.com website.)
For errata for the 4th edition, send an email to firstname.lastname@example.org. Type Errata in the subject line; no message necessary.
Part I Prologue
1 Basic Properties of Numbers
2 Numbers of Various Sorts
Part II Foundations
Appendix. Ordered Pairs
Appendix 1. Vectors
Appendix 2. The Conic Sections
Appendix 3. Polar Coordinates
6 Continuous Functions
7 Three Hard Theorems
8 Least Upper Bounds
Appendix. Uniform Continuity
Part III Derivatives and Integrals
11 Significance of the Derivative
Appendix. Convexity and Concavity
12 Inverse Functions
Appendix. Parametric Representation of Curves
Appendix. Riemann Sums
14 The Fundamental Theorem of Calculus
15 The Trigonometric Functions
*16 Pi is Irrational
*17 Planetary Motion
18 The Logarithm and Exponential Functions
19 Integration in Elementary Terms
Appendix. The Cosmopolitan Integral
Part IV Infinite Sequences and Infinite Series
Approximation by Polynomial Functions
*21 e is Transcendental
22 Infinite Sequences
23 Infinite Series
24 Uniform Convergence and Power Series
25 Complex Numbers
26 Complex Functions
27 Complex Power Series
Part V Epilogue
29 Construction of the Real Numbers
30 Uniqueness of the Real Numbers
From the preface:
Every aspect of this book was influenced by the desire to
present calculus not merely as a prelude to but as the first real encounter with
mathematics. Since the foundations of analysis provided the arena in which
modern modes of mathematical thinking developed, calculus ought to be the place
in which to expect, rather than avoid, the strengthening of insight with logic.
In addition to developing the students' intuition about the beautiful concepts
of analysis, it is surely equally important to persuade them that precision and
rigor are neither deterrents to intuition, nor ends in themselves, but the
natural medium in which to formulate and think about mathematical questions.
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